I would say the meaning is similar but not quite the same.
I found some example sentences at https://www.wordhippo.com/what-is/sentences-with-the-word/with_this_in_mind.html
Our aim is to inform you not to irritate. With this in mind, our publication will now be sent twice monthly.
In this example, the writer is pointing out that they (the publishers) don�t want to annoy people and that�s why they are going to now send the publication twice a month. Presumably they were sending it more frequently than that.
You can�t simply substitute "knowing this" and convey the same meaning. You would need to reword it a bit. For example:
We know that some people are irritated as they feel we are sending the publication too often. Knowing this, our publication will now be sent out twice monthly.
I hope that helps!